Date: Mar 24, 2013 6:19 AM
Author: William Hughes
Subject: Re: Matheology § 224
On Mar 24, 11:04 am, WM <mueck...@rz.fh-augsburg.de> wrote:

Your proof covers all lines. We have for all lines l

of the list.

if l and all its predecessors are removed

and no other line is removed,

then the union of all lines is not changed"

However, there is no information about what will

happen if you try to apply this to two

lines e.g. l along with all its predecessors

and m along with all its predecessors.

Now it is easy to see what will happen in this

case. Since we can replace l and m with

one of either l or m, we know what will happen

if we remove two lines.

Since we can replace l,m and p with

one of either l or m or p, we know what will happen

if we remove three lines.

It is easy to see we know what

will happen if we remove a natural

number of finite lines.

However, we do not know what will happen

if we remove an infinite number of

finite lines.